[SOLVED] separable ode

A parachutist falls under gravity and the drag on the chute is known to have an air resistance which is proportional to the square of the velocity v and given by kv2 per unit mass. According to Newton’s Law of Motion the velocity of the parachutist satisfies the differential equation

dv/dt = g - kv^2

where g is a gravitational constant. Find the velocity of the particle at any time t subject to the initial condition that v=0 at t=0. Hence confirm that the velocity of the particle tends to the terminal velocity.

A parachutist falls under gravity and the drag on the chute is known to have an air resistance which is proportional to the square of the velocity v and given by kv2 per unit mass. According to Newton’s Law of Motion the velocity of the parachutist satisfies the differential equation

dv/dt = g - kv^2

where g is a gravitational constant. Find the velocity of the particle at any time t subject to the initial condition that v=0 at t=0. Hence confirm that the velocity of the particle tends to the terminal velocity.

Im finding it tricky to differentiate the dv/g-kv^2 bit

I hope what you are trying to do is integrate, not differentiate it! Since that is a rational function, you can integrate using "partial fractions". If you think of the denominator as a "difference of squares" it's easy to factor: